The other main topic that remains open is the difference found in the faint-end slope of FGs LFs. This is difficult to explain within the current models of formation and evolution of clusters. In fact, most of the studies points toward a sort of global value for the faint-end slope in clusters and groups. It is worth noting, however, that the majority of the studies of LFs in FGs used photometric data and that, in the literature, significant differences were found even in regular clusters when only photometric data were used. Thus, the next step in this discussion awaits the use of large spectroscopic datasets, that will become available with the next generation of astronomical instruments (e.g. WEAVE, 4MOST, DESI).
However, we can tentative say that the presence of radial orbits could give an answer also to the problem of the faint-end slope of the LF: in fact, if massive galaxies on radial orbits have a shorter timescale to be merged within the central galaxy, dwarf galaxies could be more easily disrupted on such orbits, if they pass near the BCG [1]}.
Another possible explanation for the differences in the galaxy populations between FGs and non-FGs could be found in the surrounding environment, since hints of different large-scale structures are found in some individual studies. In particular, we can not exclude that FGs are still in the process of accreting dwarf galaxies, but the general picture remains to be clarified.
